The second case analyzed is based on the Bose-Einstein Condensation dark matter model and can be described by the Thomas-Fermi (TF) profile, whose application is more relevant in small distances of galaxies. In fact, the interactions of dark matter particles can no longer be neglected in the inner regions of galaxies, so it ceases to be cold. The TF profile can be represented in the form [1]}
\(\rho =\rho _{TF}=\rho _{s}\frac{\sin (k r)}{kr},\) 
